An invitation to Mathematics
This book is a recopilation of 14 contributions written with the 'excuse' of the 50th International Mathematical Olympiad, which was held in Bremen (Germany) in 2009. One highlight of this olympiad was the celebration ceremony of the 50th anniversary of the IMOs. To this ceremony, six world's leading international research mathematicians who had been contestants at some previous IMO, were invited, namely: Béla Bollobás, Timothy Gowers, László Lovász, Stanislav Smirnov, Terence Tao and Jean-Christophe Yoccoz. All of them have written contributions for this volume. The other contributions are written by well-known mathematicians: Michael Stoll, Simon Norton, Alexandez Razborov, Lloyd Trefethen, Robert Kerr and Marcel Oliver, Nader Masmoudi, Günter Ziegler and Dierk Schleicher.
Each of the pieces focuses in a particular area, covering altogether a wide range of mathematics. The texts are primarily addressed to students who have participated at IMOs, although some of them are of a level a bit higher than that. The book may be nice reading for a student in a first degree of Mathematics, or for anyone with interests in mathematics in general.
Some of the texts give a general overview of a particular topic (like the theory of fractals, or the equations of fluid dynamics). Other texts start by introducing a seemingly innocent problem (of the type of those in mathematics olympiads) and follows the path that leads to some active research mathematics. Some of them contain personal comments with experiences of the authors. Personally, I have much enjoyed the piece by Timothy Gowers, where he addresses to an IMO student who may be thinking whether to choose mathematics as a carreer, and gives him or her advice based on his experience. Let me end up with one of his comments: "If you are truly interested in mathematics, then hard mathematical work does not feel like a chore: it is what you want to do."